Minimum entropy-based performance assessment of feedback control loops subjected to non-Gaussian disturbances

Abstract Control performance assessment (CPA) is a useful tool to establish the quality of industrial feedback control loops. While many current CPA techniques are developed solely for the controlled systems under the assumption of the Gaussian disturbance, the conventional minimum variance control (MVC) approach would not be applied when the disturbance distribution is non-Gaussian. In this paper, based on the information theory and the minimum entropy criterion, a more general CPA index for the feedback control loop subjected to unknown disturbance distribution is investigated. The fundamentals of MVC are first reexamined, and then an innovative performance index is given by incorporating the entropy. The feedback control algorithm based on minimum entropy, called MEC (minimum entropy control), is derived. MEC based CPA for the controlled system requires effective and systematic identification of the associated system models based on the closed-loop data. In this work, a new methodology based on the entropy criterion instead of the mean square error criterion is presented to estimate disturbances for the purpose of evaluating the performance of the control systems. To demonstrate the effective MEC based CPA method, both numerical and industrial examples are applied and compared with the MVC based CPA method.

[1]  Thomas J. Harris,et al.  Performance assessment measures for univariate feedforward/feedback control , 1993 .

[2]  T. Harris,et al.  Performance assessment measures for univariate feedback control , 1992 .

[3]  Qingfu Zhang,et al.  This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 1 RM-MEDA: A Regularity Model-Based Multiobjective Estimation of , 2022 .

[4]  J. A. Lozano,et al.  Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation , 2001 .

[5]  Christos Georgakis,et al.  Controller performance assessment based on minimum and open-loop output variance , 2000 .

[6]  David Taniar,et al.  Adaptive estimated maximum-entropy distribution model , 2007, Inf. Sci..

[7]  Michael J. Grimble,et al.  Controller performance benchmarking and tuning using generalised minimum variance control , 2002, Autom..

[8]  Deniz Erdogmus,et al.  An error-entropy minimization algorithm for supervised training of nonlinear adaptive systems , 2002, IEEE Trans. Signal Process..

[9]  Gholamhossein Yari,et al.  Some properties of Rényi entropy and Rényi entropy rate , 2009, Inf. Sci..

[10]  Shu-De Zhou,et al.  A Survey on Estimation of Distribution Algorithms , 2007 .

[11]  Mohieddine Jelali,et al.  An overview of control performance assessment technology and industrial applications , 2006 .

[12]  Hong Wang,et al.  Minimum entropy control of closed-loop tracking errors for dynamic stochastic systems , 2003, IEEE Trans. Autom. Control..

[13]  Lei Guo,et al.  Robust PDF control with guaranteed stability for non-linear stochastic systems under modelling errors , 2009 .

[14]  Biao Huang,et al.  Performance Assessment of Control Loops , 1999 .

[15]  Lei Guo,et al.  Stochastic Distribution Control System Design: A Convex Optimization Approach , 2010 .

[16]  C. T. Seppala,et al.  A review of performance monitoring and assessment techniques for univariate and multivariate control systems , 1999 .

[17]  S. Joe Qin,et al.  Control performance monitoring — a review and assessment , 1998 .

[18]  Karl Johan Åström,et al.  Computer control of a paper machine: an application of linear stochastic control theory , 1967 .

[19]  Svante Björklund,et al.  A Survey and Comparison of Time-Delay Estimation Methods in Linear Systems , 2003 .

[20]  Jizhen Liu,et al.  Minimum-Information-Entropy-Based Control Performance Assessment , 2013, Entropy.

[21]  T. Harris.  Assessment of Control Loop Performance , 1989 .

[22]  Deniz Erdogmus,et al.  Generalized information potential criterion for adaptive system training , 2002, IEEE Trans. Neural Networks.

[23]  Badong Chen,et al.  Δ-Entropy: Definition, properties and applications in system identification with quantized data , 2011, Inf. Sci..

[24]  T. J. Harris,et al.  Performance assessment of multivariable feedback controllers , 1996, Autom..

[25]  Biao Huang,et al.  Controller performance analysis with LQG benchmark obtained under closed loop conditions. , 2002, ISA transactions.

[26]  Thomas F. Edgar,et al.  Performance assessment of cascade control loops , 2000 .

[27]  Tianyou Chai,et al.  Entropy Optimization Filtering for Fault Isolation of Nonlinear Non-Gaussian Stochastic Systems , 2009, IEEE Transactions on Automatic Control.

[28]  Warren R. DeVries,et al.  Evaluation of process control effectiveness and diagnosis of variation in paper basis weight via multivariate time-series analysis , 1978 .

[29]  Junghui Chen,et al.  Minimum entropy based run-to-run control for semiconductor processes with uncertain metrology delay , 2009 .

[30]  Xin Yao,et al.  Estimation of distribution algorithms for testing object oriented software , 2007, 2007 IEEE Congress on Evolutionary Computation.

[31]  Sirish L. Shah,et al.  Feedforward plus feedback controller performance assessment of MIMO systems , 2000, IEEE Trans. Control. Syst. Technol..